This invention relates to magnetic resonance imaging and, more particularly, to a method and corresponding apparatus for capturing and providing MRI data suitable for use in a multi-dimensional imaging processes.
Magnetic resonance imaging (MRI) is a well known method of non-invasively obtaining images representative of internal physiological structures. In fact, there are many commercially available approaches and there have been numerous publications describing various approaches to MRI. Although MRI will be described herein as applying to a person""s body, it may be applied to visualize the internal structure of other objects as well, and the invention is not limited to application of MRI in a human body.
A conventional MRI system is schematically illustrated in FIG. 1. As shown in FIG. 1, an MRI system 10 includes a static magnet assembly, gradient coils, and transmit RF coils collectively denoted 12 under control of a processor 14, which typically communicates with an operator via a conventional keyboard/control workstation 16. These devices generally employ a system of multiple processors for carrying out specialized timing and other functions in the MRI system 10. Accordingly, as depicted in FIG. 1, an MRI image processor 18 receives digitized data representing radio frequency nuclear magnetic resonance responses from an object region under examination and, typically via multiple Fourier transformation processes well-known in the art, calculates a digitized visual image (e.g., a two-dimensional array of picture elements or pixels, each of which may have different gradations of gray values or color values, or the like) which is then conventionally displayed, or printed out, on a display 18a. 
A plurality of surface coils 20a, 20b . . . 20i may be provided to simultaneously acquire NMR signals for simultaneous signal reception, along with corresponding signal processing and digitizing channels.
A conventional MRI device establishes a homogenous magnetic field, for example, along an axis of a person""s body that is to undergo MRI. This magnetic field conditions the interior of the person""s body for imaging by aligning the nuclear spins of nuclei, in atoms and molecules forming the body tissue, along the axis of the magnetic field. If the orientation of the nuclear spin is perturbed out of alignment with the magnetic field, the nuclei attempt to realign their nuclear spins with an axis of the magnetic field. Perturbation of the orientation of nuclear spins may be caused by application of a radiofrequency (RF)xe2x80x94pulses. During the realignment process, the nuclei precess about the axis of the magnet field and emit electromagnetic signals that may be detected by one or more coils placed on or about the person.
It is known that the frequency of the nuclear magnetic radiation (NMR) signal emitted by a given precessing nucleus depends on the strength of the magnetic field at the nucleus"" location. Thus, as is well known in the art, it is possible to distinguish radiation originating from different locations within the person""s body simply by applying a field gradient to the magnetic field across the person""s body. For sake of convenience, this will be referred to as the left-to-right direction. Radiation of a particular frequency can be assumed to originate at a given position within the field gradient, and hence at a given left-to-right position within the person""s body. Application of a such a field gradient is referred to herein as frequency encoding.
The simple application of a field gradient does not allow two dimensional resolution, however, since all nuclei at a given left-to-right position experience the same field strength, and hence emit radiation of the same frequency. Accordingly, application of a frequency-encoding gradient, alone, does not make it possible to discern radiation originating from the top vs. radiation originating from the bottom of the person at a given left-to-right position. Resolution has been found to be possible in this second direction by application of gradients of varied strength in a perpendicular direction to thereby perturb the nuclei in varied amounts. Application of such additional gradients is referred to herein as phase encoding.
Frequency-encoded data sensed by the coils during a phase encoding step is stored as a line of data in a data matrix known as the k-space matrix. Multiple phase encoding steps must be performed to fill the multiple lines of the k-space matrix. An image may be generated from this matrix by performing a Fourier transformation of the matrix to convert this frequency information to spatial information representing the distribution of nuclear spins or density of nuclei of the image material.
MRI has proven to be a valuable clinical diagnostic tool for a wide range of organ systems and pathophysiologic processes. Both anatomic and functional information can be gleaned from the data, and new applications continue to develop as the technology and techniques for filling the k-space matrix improve. As technological advances have improved achievable spatial resolution, for example, increasingly finer anatomic details have been able to be imaged and evaluated using MRI.
Often, however, there is a tradeoff between spatial resolution and imaging time, since higher resolution images require a longer acquisition time. This balance between spatial and temporal resolution is particularly important in cardiac MRI, where fine details of coronary artery anatomy, for example, must be discerned on the surface of a rapidly beating heart. A high-resolution image acquired over a large fraction of the cardiac cycle will be blurred and distorted by bulk cardiac motion, whereas a very fast image may not have the resolution necessary to trace the course and patency of coronary arteries.
Imaging time is largely a factor of the speed with which the MRI device can fill the k-space matrix. In conventional MRI, the k-space matrix is filled one line at a time. Although many improvements have been made in this general area, the speed with which the k-space matrix may be filled is limited by, e.g., the intervals necessary to create, switch or measure the magnetic fields or RF signals involved in data acquisition, as well as physiological limits on the maximum strength and variation of magnetic fields and RF signals the human body is able to withstand.
To overcome these inherent limits, several techniques have been developed to simultaneously acquire multiple lines of data for each application of a magnetic field gradient. These techniques, which may collectively be characterized as xe2x80x9cparallel imaging techniques,xe2x80x9d use spatial information from arrays of RF detector coils to substitute for encoding which would otherwise have to be obtained in a sequential fashion using field gradients and RF pulses. The use of multiple effective detectors has been shown to multiply imaging speed, without increasing gradient switching rates or RF power deposition.
The first in vivo images using the parallel MR imaging approach were obtained using the SMASH (SiMultaneous Acquisition of Spatial Harmonics) technique. The history of parallel imaging in general and of the SMASH technique in particular is described in greater detail in U.S. Pat. No. 5,910,728, the content of which is hereby incorporated by reference. An alternative strategy for parallel imaging, known as xe2x80x9csubencodingxe2x80x9d, had been described earlier using phantom images only. A technique closely related to subencodingxe2x80x94the SENSE (SENSitivity Encoding) techniquexe2x80x94has recently been described and applied to in vivo imaging. The SENSE technique is discussed in more detail in International Publication Number WO 99/54746, the content of which is hereby incorporated by reference.
Parallel imaging techniques have tended to fall into one of two general categories, as exemplified by the SMASH and the subencoding/SENSE methods, respectively. SMASH operates primarily on the k-space matrix and is referred to herein as operating in xe2x80x9ck-space.xe2x80x9d Subencoding/SENSE, by contrast, operate primarily on data that has been transformed via one or more Fourier transforms into image data, and will be referred to herein as operating in the xe2x80x9cimage domain.xe2x80x9d
SMASH uses spatial information from an array of RF coils to obtain one or more lines of k-space data traditionally generated using magnetic field gradients, thereby allowing multiple phase encoding steps to be performed in parallel rather than in a strictly sequential fashion. To date, this parallel data acquisition strategy has resulted in up to five-fold accelerations of imaging speed and efficiency in vivo, and has enabled up to eight-fold accelerations in phantoms using specialized hardware.
SMASH is based on the principle that combinations of signals from component coils in an array may be formed to mimic the sinusoidal spatial modulations (or xe2x80x9cspatial harmonicsxe2x80x9d) imposed by field gradients, and that these combinations may be used to take the place of time-consuming gradient steps. Spatial harmonic fitting is a fundamental step in SMASH image reconstructions. This fitting procedure is designed to yield the linear combinations of coil sensitivity functions C1(x,y) which most closely approximate various spatial harmonics of the field of view (FOV):                                           ∑                          l              =              1                        L                    ⁢                      xe2x80x83                    ⁢                                    n              l                              (                m                )                                      ⁢                                          C                l                            ⁡                              (                                  x                  ,                  y                                )                                                    ≈                              C            0                    ⁢                      exp            ⁡                          (                              ⅈ                ⁢                                  xe2x80x83                                ⁢                m                ⁢                                  xe2x80x83                                ⁢                Δ                ⁢                                  xe2x80x83                                ⁢                                  k                  y                                ⁢                y                            )                                                          (        1        )            
Here, m is an integer indicating the order of the spatial harmonic, l is a coil index running from 1 to the number of coils L, n1(m) are complex fitting coefficients, and xcex94ky=2xcfx80/FOV.
FIGS. 2 and 3 demonstrate the spatial harmonic fitting procedure schematically for a set of eight rectangular coils 20a, 20b. . . 20h laid end-to-end, with a slight overlap. As shown in FIG. 3a, each coil 20a, 20b . . . has a sensitivity curve a, b . . . which rises to a broad peak directly under the coil and drops off substantially beyond the coil perimeter. The sum of the coil sensitivities form a relatively constant sensitivity, over the width of the array, corresponding to the zeroth spatial harmonic. FIGS. 3a-3e illustrate recombinations of different ones of these individual offset but otherwise similar coil sensitivity functions into a new synthetic sinusoidal spatial sensitivity. Different weightings of the individual component coil sensitivities lead to net sensitivity profiles approximating several spatial harmonics. Coil sensitivities (modeled schematically for FIGS. 3a-3e as Gaussian in shape, though in practice their shapes are somewhat more complicated and they may have both real and imaginary components) may thereby be combined to produce harmonics at various fractions of the fundamental spatial wavelength xcexy=2xcfx80/Ky, with xcexy being on the order of the total coil array extent in y. Weighted individual coil sensitivity profiles are depicted as thin solid lines beneath each component coil. Dashed lines represent the sinusoidal or consinusoidal weighting functions. Combined sensitivity profiles are indicated by thick solid lines. These combined profiles closely approximate ideal spatial harmonics across the array. A total of five spatial harmonics are shown here, but in general the maximum number of such independent combinations which may be formed for any given array is equal to the number of array elements (in this case, eight).
Once fitting coefficients satisfying Eq. (1) have been identified, a similar weighting of measured MR signals S1(kx,ky) from an image plane with spin density xcfx81(x,y) yields composite signals shifted by an amount xe2x88x92mxcex94ky in k-space:             xe2x80x83        ⁢          (      2      )                                                              ∑                              l                =                1                            L                        ⁢                          xe2x80x83                        ⁢                                          n                l                                  (                  m                  )                                            ⁢                                                S                  l                                ⁡                                  (                                                            k                      x                                        ,                                          k                      y                                                        )                                                              =                      xe2x80x83                    ⁢                                    ∑                              l                =                1                            L                        ⁢                          xe2x80x83                        ⁢                                          n                l                                  (                  m                  )                                            ⁢                              ∫                                  ∫                                                            ⅆ                      x                                        ⁢                                          ⅆ                      y                                        ⁢                                          xe2x80x83                                        ⁢                                                                  C                        l                                            ⁡                                              (                                                  x                          ,                          y                                                )                                                              ⁢                                          ρ                      ⁡                                              (                                                  x                          ,                          y                                                )                                                              ⁢                                          exp                      ⁡                                              (                                                                                                            -                              ⅈ                                                        ⁢                                                          xe2x80x83                                                        ⁢                                                          k                              x                                                        ⁢                            x                                                    ,                                                                                    -                              ⅈ                                                        ⁢                                                          xe2x80x83                                                        ⁢                                                          k                              y                                                        ⁢                            y                                                                          )                                                                                                                                                              =                      xe2x80x83                    ⁢                      ∫                          ∫                                                ⅆ                  x                                ⁢                                  ⅆ                  y                                ⁢                                  xe2x80x83                                ⁢                                  (                                                            ∑                                              l                        =                        1                                            L                                        ⁢                                          xe2x80x83                                        ⁢                                                                  n                        l                                                  (                          m                          )                                                                    ⁢                                                                        C                          l                                                ⁡                                                  (                                                      x                            ,                            y                                                    )                                                                                                      )                                ⁢                                  ρ                  ⁡                                      (                                          x                      ,                      y                                        )                                                  ⁢                                  exp                  ⁡                                      (                                                                                            -                          ⅈ                                                ⁢                                                  xe2x80x83                                                ⁢                                                  k                          x                                                ⁢                        x                                            ,                                                                        -                          ⅈ                                                ⁢                                                  xe2x80x83                                                ⁢                                                  k                          y                                                                                      )                                                                                                                    ≈                      xe2x80x83                    ⁢                      ∫                          ∫                                                ⅆ                  x                                ⁢                                  ⅆ                  y                                ⁢                                  xe2x80x83                                ⁢                                  C                  0                                ⁢                                  exp                  ⁡                                      (                                          ⅈ                      ⁢                                              xe2x80x83                                            ⁢                      m                      ⁢                                              xe2x80x83                                            ⁢                      Δ                      ⁢                                              xe2x80x83                                            ⁢                                              k                        y                                            ⁢                      y                                        )                                                  ⁢                                  ρ                  ⁡                                      (                                          x                      ,                      y                                        )                                                  ⁢                                  exp                  ⁡                                      (                                                                                            -                          ⅈ                                                ⁢                                                  xe2x80x83                                                ⁢                                                  k                          x                                                ⁢                        x                                            ,                                                                        -                          ⅈ                                                ⁢                                                  xe2x80x83                                                ⁢                                                  k                          y                                                ⁢                        y                                                              )                                                                                                                    =                      xe2x80x83                    ⁢                      ∫                          ∫                                                ⅆ                  x                                ⁢                                  ⅆ                  y                                ⁢                                  xe2x80x83                                ⁢                                  C                  0                                ⁢                                  ρ                  ⁡                                      (                                          x                      ,                      y                                        )                                                  ⁢                                  exp                  ⁡                                      (                                                                                            -                          ⅈ                                                ⁢                                                  xe2x80x83                                                ⁢                                                  k                          x                                                ⁢                        x                                            ,                                                                        -                          ⅈ                                                ⁢                                                  xe2x80x83                                                ⁢                                                  (                                                                                    k                              y                                                        -                                                          m                              ⁢                                                              xe2x80x83                                                            ⁢                              Δ                              ⁢                                                              xe2x80x83                                                            ⁢                                                              k                                y                                                                                                              )                                                ⁢                        y                                                              )                                                                                                                    =                      xe2x80x83                    ⁢                                    S              composite                        ⁡                          (                                                k                  x                                ,                                                      k                    y                                    -                                      m                    ⁢                                          xe2x80x83                                        ⁢                    Δ                    ⁢                                          xe2x80x83                                        ⁢                                          k                      y                                                                                  )                                          
This k-space shift has precisely the same form as the phase-encoding shift produced by evolution in a field gradient of magnitude xcex3Gt=xe2x88x92mxcex94ky (where y is the gyromagnetic ratio, G the magnitude of the gradient, and t the time spent in the gradient). Thus, the coil-encoded composite signals may be used to take the place of omitted gradient steps, thereby reducing the data acquisition time by multiplying the amount of spatial information gleaned from each phase encoding step. SMASH takes its cue from the physical model of gradient phase encoding, transforming the localized coil sensitivities into extended composite phase modulations (Eq.(1)) which can serve as supplementary effective gradient sets operating in tandem with the applied field gradients.
Several of the steps in the SMASH reconstruction procedure are summarized in FIGS. 4a-4c and 5a-5c, which illustrate a SMASH reconstruction with acceleration factor M=2 using a 3-element RF coil array. FIGS. 4a-4c show a k-space schematic, and FIGS. 5a-5c show image data from a water phantom at each of the corresponding stages of reconstruction. With the necessary weights in hand, MR signal data are acquired simultaneously in the coils of the array. A fraction 1/M of the usual number of phase encoding steps are applied, with M times the usual spacing in k-space (FIG. 4a). The component coil signals acquired in this way correspond to aliased images with a fraction 1/M of the desired field of view (FIG. 5a). With 1/M times fewer phase encoding steps, only a fraction 1/M of the time usually required for this FOV is spent on data collection. Next, the appropriate M linear combinations of the component coil signals are formed, to produce M shifted composite signal data sets (FIG. 4b). The composite signals are then interleaved to yield the full k-space matrix (FIG. 4c), which is Fourier transformed to give the reconstructed image (FIG. 5c, right). It should be noted that the combination of component coil signals into composite shifted signals may be performed in real time as the data arrives, or after the fact via postprocessing as is appropriate or convenient with the apparatus and the calibration information at hand.
As discussed above, SMASH is one member of a family of parallel imaging techniques including subencoding and SENSE.
The subencoding image reconstruction begins at the same starting point as a SMASH reconstructionxe2x80x94namely, with a set of component coil signals acquired using a reduced number of phase encoding gradient steps. Fourier transformation of these signal sets results in aliased component coil images like those shown in FIG. 5a. From that point on, the subencoding reconstruction operates entirely in the image domain, by combining individual pixel data in each of the aliased component coil images to extract an unaliased full-FOV image.
The basis of the technique lies in the fact that each pixel in an aliased image is in fact a superposition of multiple pixels from a corresponding full unaliased image (FIG. 5). In other words, as a result of Nyquist aliasing, an M-times aliased image Ifold is related to the putative full image Ifull as follows:                                           I            fold                    ⁡                      (                          x              ,              y                        )                          =                                                            I                full                            ⁡                              (                                  x                  ,                  y                                )                                      +                                          I                full                            ⁡                              (                                  x                  ,                                      y                    +                                          Δ                      ⁢                                              xe2x80x83                                            ⁢                      y                                                                      )                                      +                                          I                full                            ⁡                              (                                  x                  ,                                      y                    +                                          2                      ⁢                      Δ                      ⁢                                              xe2x80x83                                            ⁢                      y                                                                      )                                      +            ⋯                    =                                    ∑                              m                =                0                                            M                -                1                                      ⁢                          xe2x80x83                        ⁢                                          I                full                            ⁡                              (                                  x                  ,                                      y                    +                                          m                      ⁢                                              xe2x80x83                                            ⁢                      Δ                      ⁢                                              xe2x80x83                                            ⁢                      y                                                                      )                                                                        (        3        )            
When Ifold is acquired using a single coil, this superposition cannot be xe2x80x9cunfoldedxe2x80x9d without a priori knowledge of the full image.
The situation changes when an array of coils is used. The full image Ilfull in each coil l is actually made up of two piecesxe2x80x94the spin density xcfx81, and the coil sensitivity function Cl:
Ilfull(x,y)=Cl(x,y)xcfx81(x,y)xe2x80x83xe2x80x83(4)
and in an array, each component coil l has a different sensitivity Cl. Thus, each coil presents one of multiple xe2x80x9cviewsxe2x80x9d of the aliasing, which can be used to deduce just how much of each aliased pixel belongs at any position in the full image. Substituting Eq. (4) into Eq. (3) gives                                           I            l            fold                    ⁡                      (                          x              ,              y                        )                          =                                            ∑                              m                =                0                                            M                -                1                                      ⁢                          xe2x80x83                        ⁢                                          I                l                full                            ⁡                              (                                  x                  ,                                      y                    +                                          m                      ⁢                                              xe2x80x83                                            ⁢                      Δ                      ⁢                                              xe2x80x83                                            ⁢                      y                                                                      )                                              =                                    ∑                              m                =                0                                            M                -                1                                      ⁢                          xe2x80x83                        ⁢                                                            C                  l                                ⁡                                  (                                      x                    ,                                          y                      +                                              m                        ⁢                                                  xe2x80x83                                                ⁢                        Δ                        ⁢                                                  xe2x80x83                                                ⁢                        y                                                                              )                                            ⁢                              ρ                ⁡                                  (                                      x                    ,                                          y                      +                                              m                        ⁢                                                  xe2x80x83                                                ⁢                        Δ                        ⁢                                                  xe2x80x83                                                ⁢                        y                                                                              )                                                                                        (        5        )            
where xcex94y=FOVy/M. For any particular aliased pixel (x,y), this may be written as follows:                               I          l          fold                =                                            ∑                              m                =                0                                            M                -                1                                      ⁢                          xe2x80x83                        ⁢                          I                              l                ⁢                                  xe2x80x83                                ⁢                m                            full                                =                                    ∑                              m                =                0                                            M                -                1                                      ⁢                          xe2x80x83                        ⁢                                          C                                  l                  ⁢                                      xe2x80x83                                    ⁢                  m                                            ⁢                              ρ                m                                                                        (        6        )            
where Ilmfullxe2x89xa1Ilfull(x,y+mxcex94y), Clmxe2x89xa1Cl(x,y+mxcex94y), and xcfx81mxe2x89xa1xcfx81(x,y+mxcex94y).
For example, in a four-coil array, using a factor of three aliasing (FIG. 6):
I1fold=C11xcfx811+C12xcfx812+C13xcfx813
I2fold=C21xcfx811+C22xcfx812+C23xcfx813xe2x80x83xe2x80x83(7)
I3fold=C31xcfx811+C32xcfx812+C33xcfx813
I4fold=C41xcfx811+C42xcfx812+C43xcfx813
This equation may be rewritten in matrix form as                               [                                                                      I                  1                  fold                                                                                                      I                  2                  fold                                                                                                      I                  3                  fold                                                                                                      I                  4                  fold                                                              ]                =                              [                                                                                C                    11                                                                                        C                    12                                                                                        C                    13                                                                                                                    C                    21                                                                                        C                    22                                                                                        C                    23                                                                                                                    C                    31                                                                                        C                    32                                                                                        C                    33                                                                                                                    C                    41                                                                                        C                    42                                                                                        C                    43                                                                        ]                    ·                      [                                                                                ρ                    1                                                                                                                    ρ                    2                                                                                                                    ρ                    3                                                                        ]                                              (        8        )            
or, in other words,
Ifold=Cxc2x7xcfx81xe2x80x83xe2x80x83(9)
As long as the number of coils Nc is greater than or equal to the aliasing factor M (as in our exemplary case for which Nc=4, M=3), Eq. (9) may be inverted:
xcfx81=Cxe2x88x921xc2x7Ifoldxe2x80x83xe2x80x83(10)
and the unaliased spin density xcfx81 over the full FOV may be determined.
SENSE uses an image reconstruction procedure similar to the image domain subencoding reconstruction. The SENSE technique also incorporates an in vivo sensitivity calibration method in which full-FOV component coil images are divided by an additional full-FOV body coil image, and the quotient images are then subjected to several stages of interpolation, filtering, and thresholding.
All parallel MR imaging techniques use spatial information from coil arrays to perform spatial encoding, and all require knowledge of component coil sensitivity information. Each technique has a different susceptibility to noise and/or to systematic errors in the measured sensitivity information. The physical model underlying SMASH aligns naturally with the hardware and software of a gradient-encoded MR acquisition, and the spatial harmonic fitting procedure provides a degree of noise smoothing and numerical conditioning which may be particularly important at high acceleration factors. These advantages come at the expense of introducing the approximation in Eq. (1).
The SMASH image reconstruction procedure, as described above and as described more fully in U.S. Pat. No. 5,910,728, has several potential limitations, especially where it is necessary to fit spatial harmonics to highly oblique and double oblique image planes. Since clinical imaging requires flexible image plane selection, some improvements to the basic SMASH reconstruction procedure have been called for in the course of clinical implementation.
The subencoding and SENSE image reconstruction procedure also has a number of potential limitations. It can suffer from numerical instabilities, especially when the component coil sensitivities are either insufficiently well characterized or insufficiently distinct from one another. These instabilities may manifest as localized artifacts in the reconstructed image, or may result in degraded signal to noise ratio (SNR). SENSE, in particular, conventionally requires the acquisition of additional sensitivity reference data in a coil with uniform sensitivity such as a body coil (which typically encircles the entire patient in the magnet bore). This additional reference data is used as a control for the measured sensitivities in the coil array. However, acquisition of this additional reference data, not required in SMASH, can add to the total MR examination time, and appropriate correction for this reference in the SENSE reconstruction can lengthen image reconstruction times and complicate the reconstruction algorithm. Furthermore, even with use of the body coil reference in SENSE, regions of low reference signal can result in image artifacts and miscalibrations.
The overall flexibility of SMASH image reconstructions is improved by taking advantage of various degrees of freedom in the fitting of coil sensitivities to spatial harmonics which forms the basis of the SMASH technique. Further improvements are achieved by adding numerical conditioning methods to the spatial harmonic fit, so as to bias the reconstruction towards higher SNR.
Image domain techniques are also improved by the addition of numerical conditioning. This conditioning, in combination with some additional modifications eliminates the need to acquire a body coil reference, and facilitates the treatment of regions with low intrinsic sensitivity.
Hybrid parallel imaging techniques are also described. These hybrid techniques combine some of the features and advantages of both the k-space and the image domain approaches.
According to one embodiment of the invention, a magnetic resonance image is formed by measuring RF signals in an array of RF coils, forming a set of spatial harmonics and tailoring the set of spatial harmonics to form a set of tailored spatial harmonics that are adjusted for variations in angulation of the image plane, the field of view, or the coil sensitivity calibration. In this embodiment, the coil calibration coefficients are determined by performing a spatial harmonic fit of the coil spatial sensitivities to the set of tailored spatial harmonics, and applying the determined coil calibration coefficients to the measured RF signals to form multiple lines of k-space data. The multiple lines of the k-space data are then transformed to form the MRI image.
The spatial harmonics may be tailored in a number of ways. For example, the spatial harmonics may be tailored by selecting automatically a subset of the set of formed spatial harmonics, by adjusting the set of spatial harmonics by a function not equal to 1, to adjust for sensitivity variations along a phase encode direction, and/or by performing separate spatial harmonic fits of the coil sensitivities at different spatial positions to the set of tailored spatial harmonics.
The magnetic resonance image may further be formed by adjusting each coil spatial sensitivity by a function not equal to 1, and adjusting the spatial harmonics by the same function. This function may represent the differences between component coil images, such that the importance of features shared by all component coils is minimized. Thus, in vivo sensitivity references may be used to form the magnetic resonance image.
According to another embodiment of the invention, a magnetic resonance image is formed from an array of receiving coils having distinct spatial sensitivities by forming a sensitivity matrix representing measured coil sensitivities, conditioning the sensitivity matrix, and using the conditioned sensitivity matrix during a reconstruction on signals provided by the receiving coils to form a MRI image.
In this embodiment, the sensitivity matrix may be conditioned by adding artificial orthogonal interferants to prevent generation of unduly large weights resulting from small eigenvalues in the sensitivity matrix. The eigenvalues also may be conditioned by determining eigenvalues of the sensitivity matrix and setting all eigenvalues below a threshold to a particular value, eliminating all eigenvalues below the threshold, or adding the threshold value to all eigenvalues.
According to another embodiment of the invention, a magnetic resonance image is formed from an array of receiving coils having unique spatial sensitivities by obtaining a reference image set, conditioning the reference image set, measuring RF signals indicative of nuclear spins simultaneously in each of the plurality of RF receiving coils, performing a Fourier transform on the signals from each coil to form aliased component coil image data signals, unaliasing the image data signals using the reference image set to form reconstructed component coil images, and combining the reconstructed component coil images.
According to another embodiment of the invention, a magnetic resonance image is formed from an array of receiving coils having unique spatial sensitivities by measuring MR signals indicative of nuclear spins in the plurality of receiver coils to form a set of MR signals, generating a set of encoding functions representative of a combination of spatial distributions of receiver coil sensitivities with spatial modulations corresponding to the gradient encoding steps, transforming the set of encoding functions to generate a new set of functions representative of distinct spatial positions in an image, and applying the new set of functions to the set of MR signals to form the magnetic resonance image.
According to another embodiment of the invention, a magnetic resonance image is formed from an array of receiving coils having unique spatial sensitivity by forming an encoding matrix, each entry of the encoding matrix including a coil sensitivity of a respective coil combined with a gradient modulation corresponding to a particular gradient encoding step, inverting the encoding matrix to form an inverted encoding matrix, forming a k-space matrix, each entry of the k-space matrix including a measured RF signal indicative of nuclear spins sensed by a respective coil at a particular gradient encoding step, and multiplying the inverted encoding matrix with the k-space matrix to form the magnetic resonance image. The encoding matrix may be inverted in sub-blocks, and these sub-blocks may be used to form the magnetic resonance image.